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Math Help - Integral Curves Equations

  1. #1
    Member Awsom Guy's Avatar
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    Integral Curves Equations

    Question:
    For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

    I know that y'= 4x + C
    But I don't what to do next and how to place these points to find the equation.
    Any help io good.
    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    Question:
    For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

    I know that y'= 4x + C
    But I don't what to do next and how to place these points to find the equation.
    Any help io good.
    Thanks
    find y.

    then, use the given points to set up two simultaneous equations to find the arbitrary constants of integration.
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  3. #3
    Member Awsom Guy's Avatar
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    Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
    Thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
    Thanks
    no, you found y', you need to integrate that to get to y. you will get another arbitrary constant, call it D. then solve for C and D using the points you were given.
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  5. #5
    Member Awsom Guy's Avatar
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    Do I sub in the x values aswell.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    Do I sub in the x values aswell.
    when you have y, you sub in corresponding x and y values at the same time. your last two equations must only have C and D as unknowns. that's how you'll manage to solve for them
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  7. #7
    Member Awsom Guy's Avatar
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    but I will have town unknown values C and D how am I meant to figure out the two values:
    The answers:
    -12=C+D and
    -13=C+D
    How does this help.
    Thanks
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    but I will have town unknown values C and D how am I meant to figure out the two values:
    The answers:
    -12=C+D and
    -13=C+D
    How does this help.
    Thanks
    your second equation is not right. and you've solved simultaneous equations before, yeah? That's definitely something you'd have to have done before calculus.
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  9. #9
    Member Awsom Guy's Avatar
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    What is the second equation then?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    What is the second equation then?
    tell me what expression you got for y
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  11. #11
    Member Awsom Guy's Avatar
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    I got:
    y=2x^2 + C + D.
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  12. #12
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    I got:
    y=2x^2 + C + D.
    it should be 2x^2 + Cx + D
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  13. #13
    Member Awsom Guy's Avatar
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    How does that help though
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  14. #14
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    How does that help though
    fix your second equation now and see.

    you can subtract one from the other to start finding your unknowns
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  15. #15
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    yes I got it thanks.
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